A painter has been hired to paint a wall for 2 dollars per square

Question

A painter has been hired to paint a wall for 2 dollars per square meter. How much would the painter get for painting the wall?

(1) It will take the painter three hours less to paint the wall at an average rate of 18 square meters per hour than at an average rate of 12 square meters per hour.

(2) It will take the painter 4.5 hours to paint one-fourth of the wall at an average rate of 6 square meters per hour.

Bunuel · Accepted Answer

Official Solution:

A painter has been hired to paint a wall for 2 dollars per square meter. How much would the painter get for painting the wall? 
 
Since we are given the price per square meter, we only need to find the area of the wall to get the payment amount.
 
(1) It will take the painter three hours less to paint the wall at an average rate of 18 square meters per hour than at an average rate of 12 square meters per hour.
 
Assuming that at the rate of 12 square meters per hour it would take the painter  t  hours to paint the wall, we have:  12t = 18(t-3) . Solving, we get  t = 9 . Therefore, the area of the wall is  12 * 9 = 108  square meters. Sufficient.
 
(2) It will take the painter 4.5 hours to paint one-fourth of the wall at an average rate of 6 square meters per hour.
 
This implies that to paint the whole wall it would take  4.5 * 4 = 18  hours. At a rate of 6 square meters per hour, the area of the wall is  18 * 6 = 108  square meters. Sufficient.

Answer: D

manoj2025 · Answer

IMO D. We can get total work done and multiply with 2 dolars.

awaikar · Answer

Answer is D. We need the total area of the wall to know how much will the painter be paid.
Statement 1: Let A be the area of the wall. Time taken to paint at 18 m^2/hr = A/18 | at 12, it will be A/12 --> (A/12) - (A/18) = 3. Which gives the value of A.
Statement 2: 1/4 wall is painted in 4.5 hrs at 6m^2/hr--> (A/4) = 6*4.5 --> A = 6*4.5*4.

Dereno · Answer

Paint a wall @ 2 dollars per square meter.

Amount to paint the Wall ?

Statement 1:

(1) It will take the painter three hours less to paint the wall at an average rate of 18 square meters per hour than at an average rate of 12 square meters per hour.

Let the rate of A be 18 sqm per hour

Let the rate of B be 12 sqm per hour

Tb - Ta = 3

(W/12) - (W/18) = 3

6W = 3*12*18

W = 108 Sqm.

Amount is $2 per sqm. Total amount = 108*2 = $216. Hence,  Sufficient.

Statement 2:

(2) It will take the painter 4.5 hours to paint one-fourth of the wall at an average rate of 6 square meters per hour.

1/4*W = 6*4.5

W = 6* 4.5 * 4

W = 108 sq.m

Amount is $2 per sqm. Total amount = 108*2 = $216 .  Hence,  Sufficient.

Option D

A painter has been hired to paint a wall for 2 dollars per square

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GMAT Data Sufficiency (DS) Questions

A painter has been hired to paint a wall for 2 dollars per square

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